I like Mountain Mist Blue Ribbon 100% cotton batting best for baby quilts. It is quite thin, can be quilted closely, and the quilt comes out of the washer/dryer very soft and flexible. It is a traditional batting; many antique quilts were made with it. It needs to be quilted no further than 2" apart. It is not needlepunched.
I think that Quilter's Dream Select would be very similar, and probably also Mountain Mist Cream Rose or White. These are also thin cotton battings, but have been needlepunched for additional stability so quilting lines do not need to be as close together.
One of the reasons Warm and Natural is stiffer is because it has been needlepunched through scrim. The other battings I mentioned have no scrim.